Should Type Theory replace Set Theory as the Foundation of Mathematics
Thorsten Altenkirch
TL;DR
This paper argues that Type Theory offers a more suitable foundation for mathematics than Set Theory, emphasizing its advantages in consistency and expressiveness.
Contribution
It presents a comparative analysis highlighting the benefits of Type Theory over Set Theory as a foundational framework.
Findings
Type Theory provides better consistency for mathematical foundations.
Type Theory enhances expressiveness and formalization capabilities.
The paper advocates for adopting Type Theory as the primary foundation.
Abstract
We discuss why Type Theory is preferable as foundation of Mathematics compared to set theory.
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Taxonomy
TopicsComputability, Logic, AI Algorithms